With a deep floor flange Or a wax seal with a horn and extra long Brass floor flange bolts
You can install the vanity first. Then, install the tile up to the vanity and around the pipe for the toilet. Then, install the toilet. That way, you do not have to replace the tile should you ever have to replace the toilet.
If you are installing a floating laminate floor, you can easily put it right over the tile.
twice the material
Inside pipe cutter
People generally charge extra when more work is involved. This is a good case - is it easier to remove and replace the toilet and lay the tiles intact than it is to leave the toilet in place and try to cut the tiles to fit around it? Having recently tiled by own bathroom floor, it was easier to remove the toilet and lay the 'whole' tiles and then to replace the toilet when the cement and grout had dried. (Then I ran some sealant around the join to prevent dirt catching, and to make cleaning the floor eaiser.)
You can replace just one tile without too much grief. First you need to obtain a look alike tile. Then you need to chisel the existing tile out. Put the new one and regrout with comparable grout as used before.
Remove the toilet from the floor, locate the broken tip, and replace the toilet. Don't forget the new wax ring.
Pull the toilet. Check the closet flange. If it is not loose or broken, replace the wax ring and closet bolts. Reset toilet. Level with wobble wedges. Caulk base of toilet.
There is no reason to wax a tile floor.
Only if someone puts it there! It is not a naturally occurring item in a toliet! Depending on when the toilet room was built, asbestos might be found in the floor tile or glue holding the floor tile in place, in the wall board or spackling compound, in the textured plaster, in the glue securing the baseboard, or in the caulking compound used around the tub or window.
The toilet should sit on top of the new tile.
Where is it leaking ? Flapper in the tank, replace flapper. Between tank and bowl, separate and replace the seal. Toilet to floor. Replace the wax ring under the toilet, making sure it is thick enough to form a seal and the bolts are installed correctly and holding the toilet down.